Rank-Adaptive Tensor Methods for High-Dimensional Nonlinear PDEs

We present a new rank-adaptive tensor method to compute the numerical solution of high-dimensional nonlinear PDEs. The method combines functional tensor train (FTT) series expansions, operator splitting time integration, and a new rank-adaptive algorithm based on a thresholding criterion that limits...

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Bibliographic Details
Published in:	Journal of scientific computing Vol. 88; no. 2; p. 36
Main Authors:	Dektor, Alec, Rodgers, Abram, Venturi, Daniele
Format:	Journal Article
Language:	English
Published:	New York Springer US 01.08.2021 Springer Nature B.V
Subjects:	Adaptive algorithms Algorithms Approximation Computational Mathematics and Numerical Analysis Covariance matrix Decomposition Energy Fokker-Planck equation Mathematical analysis Mathematical and Computational Engineering Mathematical and Computational Physics Mathematics Mathematics and Statistics Nonlinear differential equations Numerical integration Operators (mathematics) Partial differential equations Robustness (mathematics) Series expansion Tensors Theoretical Time integration Dynamical low-rank approximation Tensor train decomposition Tensor manifolds
ISSN:	0885-7474, 1573-7691
Online Access:	Get full text
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